As a background art to which this application belongs, there is a technique disclosed in JP 2008-175202 A (PTL 1). The publication discloses a technique in which a dead time of the air-fuel ratio sensor is measured from a peak variance value of an input air-fuel ratio and a peak value of an output air-fuel ratio of the air-fuel ratio sensor which detects the air-fuel ratio of an exhaust gas of an internal combustion engine, and diagnoses an abnormality.